Tag: vedic methods of multiplication

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Multiple choice vedic methods of multiplication history of mathematics maths

$\displaystyle\frac{1}{5}$ of $\displaystyle\frac{2}{7}$ of $\displaystyle \frac{8}{3}$ of $4095=?$

  1. $642$
  2. $598$
  3. $648$
  4. $475$

  5. None of these
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

$\displaystyle \frac{1}{5}$ of $\displaystyle\frac{2}{7}$ of $\displaystyle\frac{8}{3}$ of $4095$
$=\displaystyle\frac{1}{5}\times \frac{2}{7}\times \frac{8}{3}\times 4095=624$.

Hence the correct answer is option E

Multiple choice vedic methods of multiplication history of mathematics maths

The value of $3\dfrac{1}{12}$ - $\big[ 1\dfrac{3}{4} $+$\big[$ 2$\dfrac{1}{2}$ - $\big(1\dfrac{1}{2}$ - $\dfrac{1}{3}$ $\big)\big]\big]$

  1. $\dfrac{1}{2}$
  2. $2$
  3. $1$
  4. $0$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

We have, 3$\dfrac{1}{12}$ - $\bigg[$ 1$\dfrac{3}{4}$ +$\big[2\dfrac{1}{2}$ - $\big(1\dfrac{1}{2}$ - $\dfrac{1}{3}\big)\big]\bigg]$
= $\dfrac{37}{12}$ - $\bigg[$ $ \dfrac{7}{4}$ +$\big[\dfrac{5}{2}$ - $\big(\dfrac{3}{2}$ - $\dfrac{1}{3}$ $\big)\big]\bigg]$
= $\dfrac{37}{12}$ - $\bigg[\dfrac{7}{4}$ + $\big[\dfrac{5}{2}$ - $\big(\dfrac{9-2}{6}\big)\big]\bigg]$   $\bigg[ \because$ LCM of 2,3 =6$\bigg]$
= $\dfrac{37}{12}$ - $\big[\dfrac{7}{4}$ + $\big(\dfrac{5}{2}$ - $\dfrac{7}{6}\big)\big]$
=$\dfrac{37}{12}$ - $\big(\dfrac{7}{4}$ + $\big(\dfrac{15-7}{6}\big)\big]$        $\bigg[\because$ LCM of 2, 6 = 6$\bigg]$
=$\dfrac{37}{12}$ - $\big[\dfrac{7}{4}$ + $\dfrac{8}{6}$ $\big]$
= $\dfrac{37}{12}$ - $\big[\dfrac{21+16}{12}$ $\big]$            $\big[\because$ LCM of 4, 6 = 12 $\big]$
= $\dfrac{37}{12}$ - $\dfrac{37}{12}$ = 0

Multiple choice vedic methods of multiplication history of mathematics maths

Trishika bought some strawberries. $\cfrac{1}{8}$ of the strawberries were rotten and had to be thrown away. Trishika then used $25$ strawberries to bake a cake. She then had $\cfrac{1}{4}$ of the total strawberries left.
(a) How many strawberries did she have at first?
(b) If Trishika shared the remaining strawberries between her two sons equally, what fraction of the strawberries did each of them receive?

  1. $(a) 70; (b) \dfrac{1}{8}$
  2. $(a) 50; (b) \dfrac{4}{8}$
  3. $(a) 40; (b) \dfrac{1}{8}$
  4. $(a) 40; (b) \dfrac{1}{4}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Let, the total no of strawberries Trishika had $x$
No of rotten strawberries $=$ $\dfrac{1}{8}x$
No of strawberries used to bake a cake$=$25
$\therefore$ No of strawberries left$=$$x-(\dfrac{1}{8}x+25)$
A.T.Q,
$x-\dfrac{1}{8}x-25$=$\dfrac{1}{4}x$
$\implies x-\dfrac{1}{8}x-\dfrac{1}{4}x$=$25$
$\implies \dfrac{8x-x-2x}{8}$=$25$
$\implies \dfrac{5x}{8}$=$25$
$ \implies x$=$40$
b)  No of remaining strawberries $=$ $\dfrac{1}{4}x$
Shared among two sons equally$=$$\dfrac{1}{4}x \div 2$
Share of strawberries recieveed by each son$=$$\dfrac{1}{8}x$
Multiple choice vedic methods of multiplication history of mathematics maths

$\cfrac{1}{10}$ of a rod is coloured red, $\cfrac{1}{20}$ orange, $\cfrac{1}{30}$ yellow, $\cfrac{1}{40}$ green, $\cfrac{1}{50}$ blue, $\cfrac{1}{60}$ black and the rest violet. If the length of the violet portion is $12.06m$, then what is the length of the rod?

  1. $16m$
  2. $18m$
  3. $20m$
  4. $30m$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the length of the rod be $x$ $m$
$\therefore$ Length of the rod coloured be red$=\cfrac{1}{10}$ $x$ $m$
$\therefore$ Length of the rod coloured be orange$=\cfrac{1}{20}$ $x$ $m$
Length of the rod coloured be yellow$=\cfrac{1}{30}$ $x$ $m$
Length of the rod coloured be green$=\cfrac{1}{40}$ $x$ $m$
Length of the rod coloured be blue$=\cfrac{1}{50}$ $x$ $m$
Length of the rod coloured be black$=\cfrac{1}{60}$ $x$ $m$
Length of the rod coloured be violet$=12.08m$
$\therefore$ According to question
$\cfrac { 1 }{ 10 } x+\cfrac { 1 }{ 20 } x+\cfrac { 1 }{ 30 } x+\cfrac { 1 }{ 40 } x+\cfrac { 1 }{ 50 } x+12.08=x$
$\Rightarrow x-\cfrac { 49 }{ 200 } x=12.08\Rightarrow \cfrac { 151 }{ 200 } x=12.08\Rightarrow x=16$
$\therefore$ Length of the rod $=16m$

Multiple choice vedic methods of multiplication history of mathematics maths

If $'+'$ means $'\times', '-'$ means $'\div', '\times'$ means $'-'$ and $'\div'$ means $'+'$, then $2 + 15 \div 15 - 3 \times 8$ is equal to

  1. $43$
  2. $27$
  3. $35$
  4. $28$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

After interchanging the signs,
$2\times 15 + 15\div 3 - 8 = ?$
$\Rightarrow 2\times 15 + 5 - 8 = ?\Rightarrow 30 + 5 - 8 =?$
$? = 35 - 8 = 27$.

Multiple choice vedic methods of multiplication history of mathematics maths

Which of the following fraction equals $\displaystyle101\frac{3}{5}\%$

  1. $\displaystyle\frac{508}{5}$
  2. $\displaystyle\frac{254}{5}$
  3. $\displaystyle\frac{51}{25}$
  4. $\displaystyle\frac{127}{125}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$ 101 \dfrac {3}{5} = \dfrac {101 \times 5 + 3}{5} = \dfrac {505+3}{5} = \dfrac {508}{5}$

Multiple choice vedic methods of multiplication history of mathematics maths

Two candles are of different lengths and thickness. The short and the long ones can burn respectively for $3.5$ hour and $5$ hour. After burning for 2 hour, the lengths of the candles become equal in length. What fraction of the long candle's height was the short candle initially ?

  1. $\displaystyle\frac{2}{7}$
  2. $\displaystyle\frac{5}{7}$
  3. $\displaystyle\frac{3}{5}$
  4. $\displaystyle\frac{4}{5}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Shorter candle ray ${L} _{1}$ burns in 3.5 hours.
So in 2 hours $\displaystyle\frac{{L} _{1}}{3.5} \times 2$ of the candle will burn
Remaining length $= {L} _{1} - \displaystyle\frac{2{L} _{1}}{3.5} = \displaystyle\frac{1.5}{3.5}{L} _{1}$
The longer candle, ${L} _{2}$ burns in 5 hours. So in 2 hours $\displaystyle\frac{{L} _{2}}{5} \times 2$ will burn
Remaining length $= {L} _{2} - \displaystyle\frac{2{L} _{2}}{5} = \displaystyle\frac{3}{5} {L} _{2}$
Equating $\displaystyle\frac{1.5}{3.5} {L} _{1} = \displaystyle\frac{3}{5}{L} _{2}$
$\Rightarrow   \displaystyle\frac{{L} _{1}}{{L} _{2}} = \displaystyle\frac{3}{5} \times \displaystyle\frac{3.5}{1.5} = \displaystyle\frac{7}{5}$
Note : There is a mistake in question. It should read the short and the long ones can burn respectively for 5 hours and 3.56 hours. The answer $\left(\displaystyle\frac{{L} _{1}}{{L} _{2}}\right)$ will come out to be $\displaystyle\frac{5}{7}$ in that case.

Multiple choice vedic methods of multiplication history of mathematics maths

Fraction  $\displaystyle \frac { 2 }{ 5 }, \frac {3} {10} , \frac {9} {10}, \frac {16} {35} $ in ascending order are:

  1. $\displaystyle \frac { 2 }{ 5 }, \frac {3} {10} , \frac {9} {10}, \frac {16} {35} $
  2. $\displaystyle \frac { 3 }{ 10 }, \frac {2} {5}, \frac {16} {35}, \frac {9} {14} $
  3. $\displaystyle \frac { 3 }{ 10 } , \frac {9} {14} , \frac {16} {35}, \frac {2} {5} $
  4. $\displaystyle \frac { 16 }{ 35 } , \frac {2} {5} , \frac {3} {10}, \frac {9} {14} $
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The given Fraction are $\displaystyle \frac { 2 }{ 5 }, \frac {3} {10} , \frac {9} {10}, \frac {16} {35} $
LCM of 5, 10, 14, 35 = $\displaystyle (5\times 2\times 7\times)= 70 $
Now change each of the following into an equivalent fraction having 70 as its denominator.
Now, $\displaystyle \frac { 2 }{ 5 } =\frac { 2\times 14 }{ 5\times 14 } =\frac { 28 }{ 70 } \ \frac { 3 }{ 10 } =\frac { 3\times 7 }{ 10\times 7 } =\frac { 21 }{ 70 } \ \frac { 9 }{ 14 } =\frac { 9\times 5 }{ 14\times 5 } =\frac { 45 }{ 70 } \ and\quad \frac { 16 }{ 35 } =\frac { 16\times 2 }{ 35\times 2 } =\frac { 32 }{ 70 } \ Clearly,\quad \frac { 28 }{ 70 } >\frac { 21 }{ 70 } <\frac { 45 }{ 70 } >\frac { 32 }{ 70 } \ Hence,\quad \frac { 3 }{ 10 } <\frac { 2 }{ 5 } <\frac { 16 }{ 35 } <\frac { 9 }{ 14 } $

Multiple choice vedic methods of multiplication history of mathematics maths

The value of the expression $\dfrac { 1 }{ \sqrt { 11-2\sqrt { 30 }  }  } -\dfrac { 3 }{ \sqrt { 7-2\sqrt { 10 }  }  } -\dfrac { 4 }{ \sqrt { 8+4\sqrt { 3 }  }  } $ after simplification is

  1. $\sqrt { 30 } $
  2. $2\sqrt { 10 } $
  3. $1$
  4. $0$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$\dfrac { 1 }{ \sqrt { 11-2\sqrt { 30 }  }  } -\dfrac { 3 }{ \sqrt { 7-2\sqrt { 10 }  }  } -\dfrac { 4 }{ \sqrt { 8+4\sqrt { 3 }  }  } $


$=\left (\dfrac { 1 }{ { 11-2\sqrt { 30 }  }  }\right)^{\frac{1}{2}} -\left( \dfrac { 3 }{ { 7-2\sqrt { 10 }  }  }\right)^{\frac{1}{2}} -\left( \dfrac { 4 }{ { 8+4\sqrt { 3 }  }  }\right)^{\frac{1}{2}} $


$=\left (\dfrac { 1 }{ { 5+6-2\sqrt {5}\sqrt{6}}}\right)^{\frac{1}{2}} -\left( \dfrac { 3 }{ { 5+2-2\sqrt {5}\sqrt{2}}}\right)^{\frac{1}{2}} -\left( \dfrac { 4 }{ {6+2+2\sqrt {6}\sqrt{2}  }  }\right)^{\frac{1}{2}} $

$={ \left( \dfrac { 1 }{ (\sqrt { 6 } -\sqrt { 5 } )^2 }  \right)  }^{ \frac { 1 }{ 2 }  }-3{ \left( \dfrac { 1 }{( \sqrt { 5 } -\sqrt { 2 } )^2 }  \right)  }^{ \frac { 1 }{ 2 }  }-4{ \left( \dfrac { 1 }{ (\sqrt { 6 } +\sqrt { 2 } )^2 }  \right)  }^{ \frac { 1 }{ 2 }  }$

$={ \left( \dfrac { 1 }{ \sqrt { 6 } -\sqrt { 5 }  }  \right)  }^{ \frac { 2 }{ 2 }  }-3{ \left( \dfrac { 1 }{ \sqrt { 5 } -\sqrt { 2 }  }  \right)  }^{ \frac { 2 }{ 2 }  }-4{ \left( \dfrac { 1 }{ \sqrt { 6 } +\sqrt { 2 }  }  \right)  }^{ \frac { 2 }{ 2 }  }$

$={ \left( \dfrac { 1 }{ \sqrt { 6 } -\sqrt { 5 }  } \times {\dfrac{\sqrt{6}+\sqrt{5}}{\sqrt{6}+\sqrt{5}}} \right)  }^{ \frac { 2 }{ 2 }  }-3{ \left( \dfrac { 1 }{ \sqrt { 5 } -\sqrt { 2 }  } \times{\dfrac{\sqrt{5}+\sqrt{2}}{\sqrt{5}+\sqrt{2}}} \right)  }^{ \frac { 2 }{ 2 }  }-4{ \left( \dfrac { 1 }{ \sqrt { 6 } +\sqrt { 2 }  } \times{\dfrac{\sqrt{6}-\sqrt{2}}{\sqrt{6}-\sqrt{2}}} \right)  }^{ \frac { 2 }{ 2 }  }$

$=\left( \sqrt { 6 } +\sqrt { 5 }  \right) -\left( \sqrt { 5 } +\sqrt { 2 }  \right) -\left( \sqrt { 6 } -\sqrt { 2 }  \right) =0$
Hence, option D is correct.
Multiple choice vedic methods of multiplication history of mathematics maths

Which of the following statement is CORRECT?
Statement-1: Mrs. Soni bought 7$\dfrac{1}{2}$ litres of milk. Out of this, 5$\dfrac{3}{4}$ liters was consumed. 1$\dfrac{1}{3}$ liters of milk is left with her.
Statement-2: Amit reads $\dfrac{3}{5}$ of a book. He finds that there are still 80 pages left to be read. The total number of pages in the book is $200.$

  1. Only statement-1

  2. Only Statement-2

  3. Both Statement-1 and Statement-2

  4. Neither Statement-1 nor Statement-2
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Statement-1: Total quantity of milk bought = 7$\dfrac{1}{2}$litres = $\dfrac{15}{2}$litres
Quantity of milk consumed = 5$\dfrac{3}{4}$litres
                                            = $\dfrac{23}{4}$ litres
$\therefore$ Quantity of milk left = $\big(\dfrac{15}{2}$ - $\dfrac{23}{4}$$\big)$ litres
= $\big(\dfrac{30-23}{4}\big)$ litres = $\dfrac{7}{4}$ = 1$\dfrac{3}{4}$ litres
Statement-2: Let total number of pages in the book be x.
According to question,
$\dfrac{3}{5}$x + 80 = x
$\Rightarrow$ x - $\dfrac{3}{5}$x = 80 $\Rightarrow$ x = $\dfrac{80\times5}{2}$
$\Rightarrow$ x = 200
$\therefore$ Total number of pages = 200
Hence, only statements-2 is true.